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Solve xsin(y/x)dy=(ysin(y/x)-x)dx....

Solve `xsin(y/x)dy=(ysin(y/x)-x)dx`.

Text Solution

Verified by Experts

`(siny/x)(dy)/(dx) = (y/x.siny/x-1)`
Put `y=vx`
`rArr sinv(v+x(dv)/(dx))=(vsinv-1)`
or `sinv(xdv)/(dx) =-1`
or `intsinvdv=-int(dx)/(x)`
`rArr cosv=log_(e)x+c`
`rArr cosy/x=log_(e )x+c`
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